Why hair particles inside
Problems come from two issues: rotation not applied and mesh with Ngons.
To solve some of them you can:


free particle edit of your "small hair2"
select the mesh and apply rotation and scale (Ctrl+A
)
recomb your hairs


To solve all issues, do a quick retopology to have a "quads only" and "edge loops only" mesh, and exclude from the vertex group all vertices that belong to the internal, borders also (think in terms of which faces you want to emit hair).

Another workaround could be make a copy of the external part of the mesh, delete the Ngons and extrude the last circle loop to reach the position of the previous borders, assign the particle systems to the new mesh and uncheck the "emitter" option in the particle render tab, so that the new mesh will not be rendered.